# Linear Algebra true/false explanation.

#### A_lilah

Linear Algebra true/false explanation. :)

1. Homework Statement

True or False:
Is it possible to find a pair of two-dimensional subspaces S and T of R3 such that S (upside down U) = {0} ?

2. Homework Equations

3. The Attempt at a Solution

My understanding: upside down U = intersection, and for S to intersect T, S must have some vectors that are linear combinations of the vectors of T (and vice versa). These combinations have to = 0... and that's all I've got. I've sifted through my notes and the textbook several times, and the only other thing I could come up with that may or may not be useful (I haven't connected the dots yet), is that:
Def: the vectors v1, v2,...,vn in a vector space V are said to be linearly independent if
c1v1+c2v2+...+cnvn = 0
which implies that all the scalars c1...cn must equal zero

(the answer in the back of the book says that the answer is false, which is why I was looking at linear independence.)
Thanks!

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#### Mark44

Mentor
Re: Linear Algebra true/false explanation. :)

Think about the geometry of your problem. S and T are both two-dimensional subspaces of R^3, which means that both (S and T) are planes that contain the origin. Is it possible to have two planes in R^3, both containing the origin, that intersect at no other points?

#### A_lilah

Re: Linear Algebra true/false explanation. :)

No. So does = {0} mean they only contain the origin then?

#### HallsofIvy

Science Advisor
Homework Helper
Re: Linear Algebra true/false explanation. :)

Yes, {x} means a set that contains only the single member x. Surely you knew that?

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